It is usually to say that matrix \(A\)  satisfies the RIP of order \(s\)  if \(\delta _s < 1\) .
It is well known that the random matrices such as Bernoulli and Gaussian matrices are widely used in applications as they satisfy the RIP with an overwhelming probability [1]}, [2]}.
The following property of RIC is frequently used in our paper.
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Suppose matrix \(A\)  satisfy the RIP of order \(k\) .
Given a vector \(u \in \mathbb {R}^n\)  and a set \(\Omega \subseteq [N]\) , one has
